Sun imitating partially cloudy sky
To give the impression of a partially cloudy sky you could place a plane above your scene and use a Mix node to vary between Diffuse and Transparent shader using a Texture such as Musgrave or Noise as shown :



With the plane high above your scene it won’t be visible to the camera but will still affect the parallel rays of the sun lamp. Alternatively, if it would be visible to the camera due to the camera angle you could use a Light Path ‘Is Camera Ray’ node to make it fully transparent to the camera while still casting shadows.